By Etienne Forest
ISBN-10: 4431558020
ISBN-13: 9784431558026
ISBN-10: 4431558039
ISBN-13: 9784431558033
This publication illustrates a thought like minded to monitoring codes, which the writer has constructed through the years. monitoring codes now play a imperative function within the layout and operation of particle accelerators. the idea is absolutely defined step-by-step with equations and real codes that the reader can assemble and run with freely to be had compilers.
In this e-book, the writer pursues a close technique in keeping with finite “s”-maps, considering this is often extra normal so long as monitoring codes stay on the centre of accelerator layout. The hierarchical nature of software program imposes a hierarchy that places map-based perturbation concept above the other equipment. The map-based technique, maybe satirically, permits finally an implementation of the Deprit-Guignard-Schoch algorithms extra devoted than whatever present in the normal literature. This hierarchy of equipment isn't a private selection: it follows logically from monitoring codes overloaded with a truncated strength sequence algebra package.
After defining abstractly and in brief what a monitoring code is, the writer illustrates lots of the accelerator perturbation thought utilizing a precise code: PTC. This booklet could appear like a handbook for PTC; in spite of the fact that, the reader is inspired to discover different instruments in addition. The presence of a precise code guarantees that readers could have a device with which they could try out their realizing. Codes and examples could be to be had from a number of websites because PTC is in MAD-X (CERN) and BMAD (Cornell).
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Additional resources for From Tracking Code to Analysis: Generalised Courant-Snyder Theory for Any Accelerator Model
Sample text
The pendulum and the standard map are closely related examples of these two types of maps. While we would like to have integrable maps, in reality, most maps are not integrable. In this section I discuss the pendulum since it is the archetype of the integrable map in one degree of freedom. It has an obvious invariant: the Hamiltonian itself. Moreover, using mathematics of the most elementary kind, we can get the period of oscillation as a function of the initial amplitude. This period, contrary to the impression given in some high school textbook, depends on the initial amplitude.
The purpose of this section is to provide the solution of a problem that the reader could have gotten without using the tools of perturbation theory. Then, in Sect. 2, I produce the map with the package FPP. This map will be analysed with Hamiltonian methods and the result reproduced by a little algorithm in the program pendulum of Appendix E. Then, in Sect. 3, I will finally look at the standard map which is representative of an accelerator: the Hamiltonian is intrinsically s-dependent and thus new tools must be introduced if we are to stay “faithful” to the Code!
2. The trajectories are not ellipses but can be distorted into conics using symplectic transformations. In fact they can be distorted into circles. 3. These two results extend to integrable Hamiltonians in several degrees of freedom. However most Hamiltonians taken out of a hat2 are not integrable. The standard map, which is a close relative of the pendulum, is not integrable. The standard map emerges from the pendulum when we apply numerical integration to the pendulum. For example, if I use a first- or second-order symplectic integrator on the pendulum, I produce the standard map.
From Tracking Code to Analysis: Generalised Courant-Snyder Theory for Any Accelerator Model by Etienne Forest
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